4.1 angles and measures comp.notebook October 25, 2019

4.1 Angles and their Measures

Degrees & radians – two common angle measures.

A degree can be written in DMS form – Degree, Minutes and Seconds. A degree (o) is subdivided into 60 minutes (`) and each minute is subdivided into 60 seconds (``)

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Ex.1 Convert 99.37o to DMS form.

Ex.2 Convert 35024`16`` to decimal form.

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A radian is the measure of the central angle of an arc whose length is the same as it’s radius.

2π=360o

Radians ­­> Degrees Degrees ­­> Radians

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Ex.3 How many radians are in 120o?

Ex.4 How many degrees are in π/2 radians?

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Compass Bearings When working with compass bearings always start with North as 0o and work clockwise to get your angle. We always work in DEGREES for bearings.

Ex.5 Find the compass bearing that describes:

(a) SE (b) SSE (c) NW

Nov 19­7:21 PM 5 4.1 angles and measures comp.notebook October 25, 2019 Circular Arc Length

θ Central angle in rads s – arc length r – radius

Ex.6 Find the perimeter of a sector whose central angle is 30o, with radius 12.

Concentric Circles have the SAME center.

Ex.7 A central angle intercepts the arcs, s1 and s2 of two concentric circles. The inner circle has a radius of r1 of 5cm and an arc length s1 of 15cm. What is the measure of the central angle? Given that the outer circle has an arc length s2=40cm, what is its radius?

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Nautical Miles

A nautical mile is the length of 1 minute of an arc along the earth’s equator. 1 statute mile ≈ 0.87 nautical mile 1 nautical mile ≈ 1.15 statute miles

Ex.8 Mr. George flew from Boston to San Francisco a distance of 2698 statute miles. How many nautical miles is this equivalent to?

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Angular and linear motion

Ex.9 Mr. Robinette’s truck has wheels 36” in diameter and he is driving along Naranja outside IRHS. If his wheels are rotating at 320 rpm, is he speeding? (Note there are 5280ft per mile.)

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